EP0438347A1 - Method and apparatus for controlling the bedding of a post - Google Patents

Abstract

The mass M of the foundation mass (4) supporting the post (1) and the stiffness of the soil / solid mass K determined by comparing the transfer function T (w) calculated from the measurement of a vertical shock f (t ) applied to the base (2) of the post (1) and to the measurement of the corresponding vertical vibrations x (t) of the bed (4), of the theoretical transfer function (21) of a system (6) with two degrees of freedom, using a so-called modal analysis software.

Description

The invention relates to methods and devices for checking the sealing of a pole and in particular of an electric pole.

More specifically, the subject of the invention is methods and devices for determining the mass M of a foundation massif supporting a post of known mass m, and the stiffness K of the ground on this massif.

The foundation of a post, electric for example, is carried out by pouring a concrete mass in a dig. During this operation, the post is kept vertical in the center of the excavation. Among others, two faults can taint the realization of this foundation: the excavation can be of insufficient size, and / or it can be badly cleaned. In the first case the concrete block will be undersized, and in the second case, the connection between the concrete block and the soil in place will be very poor. These two faults will reduce the stability of the post. Of course, we can check the quality of the excavation before pouring the concrete and measure the weight or volume of the concrete poured to find out if the foundation is correctly made. This requires the presence of a support person during the completion of the work and this is not always possible. In addition, it may be good to check a posteriori, after the post has been sealed, that the connection between the massif and the ground remains of good quality over time.

There are known so-called vibrational analysis methods for structures according to which a structure is mechanically excited under determined and perfectly reproducible conditions, each time the mechanical excitation and mechanical response signals of the various elements of the structure are measured, these are treated measurements to deduce therefrom a transfer function which is a relationship between the mechanical response signals and the mechanical excitation signals and these measurements are repeated at time intervals.

These methods make it possible to know whether cracks have appeared in the structure. They would probably make it possible to know if the connection between the solid mass and the ground does not change over time, but they do not make it possible to know, a posteriori, the mass M of the concrete solid bearing a post of known mass m.

Indeed, in the conventional impulse method, the mass foundation of mass M is represented by a system with a degree of freedom, comprising a rigid mass M resting on a spring of stiffness K in parallel with a damper of coefficient C. The latter two elements represent the action of the ground in which the concrete block is embedded: the spring diagrams the elasticity of this ground, while the shock absorber translates the radiation of mechanical energy of which it is the seat. By giving a vertical shock f (t) at the center of the mass and by measuring the response x (t) of it, in the same place and in the same direction, we can calculate the transfer function of the system at a degree of freedom and very easily extract the parameters M, C and K.

But in the case where the massif supports a pole of mass m, we notice that the transfer function has two peaks.

The conventional impulse method described above can no longer be used to determine the mass M of the mass and the stiffness K.

The aim of the present invention is to propose a method for determining the mass M of a foundation block supporting a post of known mass m, and the stiffness of the ground / block connection K, with a view to checking, a posteriori, the sealing. pole in the ground.

et on détermine la raideur de liaison sol/massif K à l'aide de la formule exacte: $${\text{K = M(w1²+W2²) / 2-0.5 |M²(W1²-W2²)² - 4w1²w2²Mm|}}^{\text{0.5}}$$

formule à laquelle on pourra avantageusement substituer, dans les cas usuels, la formule approchée: $$\text{K = M w1²}$$

The invention achieves its object by the fact that:
said mass is mechanically excited by applying to it mechanical excitation signals f (t) along a vertical axis,
the mechanical excitation signals f (t) and the mechanical response signals x (t) are simultaneously measured along vertical axes for a period sufficient for said signals to be fully amortized,
a Fourier transformation is applied to the mechanical excitation signals f (t) and to the mechanical response signals x (t),
the transfer function T (w) is calculated by dividing the Fourier transform of the mechanical response signal by the Fourier transform of the mechanical excitation signal,
said transfer function having peaks corresponding respectively to the frequency of resonance of the solid mass when heaving and to the frequency of resonance of the post in the axial vibration mode,
we seek the theoretical curve closest to the calculated transfer function and which materializes the transfer function of a system with two degrees of freedom, respectively modeling the mass of mass M and the column of mass m,
we identify the constants (residue r1, resonance w1 and w2 and damping) of this theoretical curve,
the mass M of the foundation mass is determined using the approximate formula: $$\text{M = 1 / r1 - (1 - (w1 / w2) ²) ⁻²m}$$

and the stiffness of the soil / solid mass K is determined using the exact formula: $${\text{K = M (w1² + W2²) / 2-0.5 | M² (W1²-W2²) ² - 4w1²w2²Mm |}}^{\text{0.5}}$$

formula which can advantageously be substituted, in usual cases, the approximate formula: $$\text{K = M w1²}$$

It has in fact been found that it is more correct to represent the post and its foundation mass by a system with two degrees of freedom. The lower stage of the system models the concrete mass embedded in the ground, while the upper stage makes it possible to represent the fundamental mode of axial vibration of the post itself. The originality of the invention consists in retaining this model with two degrees of freedom for the interpretation of the measurements and the determination of the mass M of the massif and of the stiffness of the soil / massif K.

Preferably, apply the vertical shock on the face top of the foundation mass near the base of the post.

Advantageously, said vertical shock is applied using an impactor (hammer or falling mass) instrumented by a force sensor.

Advantageously, the mechanical response signals of the massif are measured by measuring the speed or the vertical acceleration of the massif at several points close to the base of the post and by averaging the measured speeds or accelerations. The speed or vertical acceleration of the massif is measured using a motion sensor (geophone or accelerometer).

In order to eliminate all the noises, the Fourier transforms are averaged for the mechanical excitation and speed (or acceleration) signals measured during several successive shocks before calculating the transfer function.

Advantageously, the values of the measurements of mechanical excitation and mechanical response signals are stored on a magnetic medium, the values stored by a computer are processed and the nearest theoretical curve is sought using software known as "d 'modal analysis or parametric identification'.

An objective of the present invention is also to propose a relatively light and inexpensive device which allows the implementation of the method.

The device according to the invention is characterized in that it comprises:
an impactor (hammer or falling mass) intended to be used to give vertical impacts on the foundation mass and instrumented by a force sensor measuring the force of the impact, at least one movement sensor (geophone or accelerometer) intended to measure the speed or acceleration of vertical displacement of the foundation mass under the action of the hammer shock, a microcomputer connected to the force sensor of the impactor and to the motion sensor via interfaces, digitizing the signals received from them corresponding to the force of the shock of the impactor and at the speed or acceleration of movement of the solid as a function of time, and capable of calculating the mass M of the foundation solid and the stiffness of the soil / solid mass K using appropriate programs.

An advantage of the invention lies in the fact that the elements of the device exist commercially and that the assembly forms a compact assembly, of low weight and easy to transport by an operator.

The following description refers to the appended drawings which represent, without any limiting nature, an example of embodiment and use of a device according to the invention.

Figure 1 schematically shows a foundation block to support a post, properly made.

Figure 2 shows, on the contrary, a mass of concrete poured into an incorrect excavation.

FIG. 3 represents the system with two degrees of freedom modeling the assembly constituted by the solid foundation and its post.

Figure 4 is a top view of the foundation block showing the preferred locations of the measuring equipment.

FIG. 5 gives the appearance of the transfer function calculated for a healthy solid mass.

Figure 6 shows the calibration of the theoretical curve of the system with two degrees of freedom.

Figure 7 shows the shape of the transfer function calculated for a defective bed.

Figure 1 shows a pole 1, which can be an electric pole or a cable car support pole for example, whose foot 2 is fixed in the ground 3 using a concrete block 4 poured into a excavation 5 The quality of the sealing of the post 1 is a function of the volume or of the mass M of the block 4 and of the quality of connection between the ground 3 and the block 4.

Figure 2 shows an example of post sealing which is carried out by a solid poured into an excavation 5 too small and poorly cleaned. Visual verification of the structure after completion does not make it possible to ensure that the mass M of the massif 4 conforms to the specifications.

FIG. 3 shows the diagram of a system 6 with two degrees of freedom which models as correctly as possible the post 1 of known mass m and its foundation 4.

The first stage of this system 6 comprises a rigid body 7 of mass M which is connected to the ground 3 by a spring 8 of stiffness K and a damper 9 of coefficient C. The spring 8 shows diagrammatically the elasticity of the ground 3 and the damper 9 reflects the radiation of mechanical energy of which it is the seat.

The second stage of this system 6 comprises a second rigid body 10 of mass m which is connected to the rigid body 7 of mass M by a spring 11 of stiffness k.

The first stage models the concrete mass 4 embedded in the ground 3 and the second stage makes it possible to represent the fundamental mode of axial vibration of the post 1.

By giving a vertical shock f (t) to the center of the rigid body 7 and by measuring the mechanical response x (t) of the latter, in the same place and in the same direction, we can calculate the transfer function T (w) of this system 6 has two degrees of freedom. This ideal transfer function presents two peaks of frequency w1 and w2 which correspond, respectively, to the natural frequency of resonance w1 of the solid mass of foundation 4 of mass M in a pounding movement, and to the natural frequency of resonance w2 of the fundamental mode of axial vibration of the pole 1. This ideal transfer function is characterized by constants such as the residue r1 associated with the frequency w1 and the frequencies w1 and w2.

et $$\text{K = M w1²}$$

We show that when the difference between w1 and w2 is large, we can relate the mechanical characteristics M and K of the solid mass + soil by approximate relations: $$\text{1 / r1 = M + (1 - (w1 / w2) ²) ⁻²m}$$

and $$\text{K = M w1²}$$

The principle of the invention consists in calculating the experimental transfer function T (w) obtained by dividing the Fourier transform of the mechanical response signal x (t) by the Fourier transform of the shock signal f (t) applied to the upper face 12 of the foundation mass 4, at draw the graph of this transfer function, find the curve of the theoretical transfer function of a system with two degrees of freedom which is closest to the curve of the transfer function resulting from experience, determine the constants r1, w1 and w2 of this theoretical transfer function and calculating the mechanical values M and K of the foundation mass. It is naturally necessary to measure the shock signals f (t) and the mechanical response signals x (t) during the duration of the experiment. The duration of the experiment is such that the mechanical response signals x (t) are completely damped at the end of the measurements.

The device according to the invention comprises an impactor which can advantageously be a hammer 14 instrumented by a force sensor, which is commonly found on the market and which will not be described further in the present description. The hammer 14 is connected by a suitable interface 15 to a microcomputer 16 which receives information concerning the shock signals f (t). The mechanical response to the shock applied by the hammer 14 on the foundation block 4 is measured by a plurality of motion sensors, geophones 17 for example, also connected to the microcomputer 16 via an interface 18. Each geophone 17 is of known type and consists of a seismic speed sensor. The microcomputer 16 is provided with means for storing data and programs. One of these so-called "modal analysis or parametric identification" programs makes it possible to search for the theoretical transfer function closest to the transfer function calculated from the data measured during the experiment.

As can be seen in FIG. 4, vertical shocks are applied at C1 in the vicinity of the base of the post 1 on the upper face 12 of the massif 4. The geophones 17, four in number in the drawing, are arranged around the post 1 and equidistant of it. The microcomputer 16 averages the response signals x (t) of the different geophones. It is also desirable, to minimize the measurement noise, to carry out several measurements x (t) following several shocks f (t), and to average the measurements made before calculating the experimental transfer function. The transfer function is calculated according to a conventional digital technique, from the self-spectra and crossed spectra of the shock and response signals.

The hammer 14 can be replaced by a falling mass instrumented by a force sensor. The geophones 14 can also be replaced by accelerometers which measure the acceleration of the movement of the massif 4 under the action of shocks.

The applicant verified the validity of his process and of the theory described above by installing two identical posts on a test area. The first of these posts was properly sealed in the ground, the excavation having been carried out under careful conditions. The second post on the contrary was badly sealed, the excavation having been deliberately carried out too small and badly cleaned. The volume of the excavations was measured before they were filled with concrete, and the quantity of concrete poured into each excavation was weighed. The weight of concrete poured into the properly completed excavation was evaluated at 23 tonnes (10 m3), compared to 9.2 tonnes poured into the deliberately bored excavation (4 m3). The method described above was applied to the two massifs.

FIG. 5 shows the transfer function 20 measured between the vertical response of the sound body along its axis and the vertical shock given at point C1. One recognizes without ambiguity the two resonances of the system, one w1 associated with the mode of heaving of the solid mass 4 and the other w2 with the mode of axial vibration of the pole 1. These two resonances have values of 35.7 Hz and 130.8 Hz. residue r1 associated with the first resonance was calculated by setting the theoretical curve 21 of the transfer function of a system with two degrees of freedom on the transfer function 20 as we see in FIG. 6. The residue r1 of this theoretical curve 21 is 3.92 10⁻⁵ m / s / N. The post having a mass of 2.8 tonnes, the calculation according to the proposed process provides for the solid mass a mass equal to 21920 kg instead of the expected 23 tonnes and a stiffness K of 1.10 10⁹ N / m.

FIG. 7 finally presents the transfer function 22 measured between the vertical response of the defective block along its axis and the vertical shock given in C1. We can still recognize, without ambiguity, the two resonances of the system (35.6 Hz and 121.2 Hz). The residue associated with the first resonance is 7.88 10⁻⁵ m / s / N. The post 1 still having a mass of 2.8 tonnes, we obtain: M = 9370 kg (for 9.2 tonnes expected) and K = 0.47 10⁹ N / m.

It can therefore be seen that the proposed method is valid for the control of the foundation solid masses 4 of posts 1. It makes it possible to quickly determine the mass M of the solid mass, and it provides an indication of the quality of the solid / soil connection. The weight of the device used is close to 10 kg, including the acquisition and processing unit. The control can be carried out by an operator alone, in a time less than a quarter of an hour per post, installation and folding of the sensors included.

Claims (8)

Method for determining the mass m of a foundation mass (4) supporting a post (1) of known mass m, and the stiffness of the soil / Mass K connection, with a view to a posteriori checking the sealing of the post (1) in the ground (3),
characterized in that
said mass (4) is mechanically excited by applying to it mechanical excitation signals f (t) along a vertical axis,
the mechanical excitation signals f (t) and the mechanical response signals x (t) are simultaneously measured along vertical axes for a period sufficient for said signals to be completely damped,
a Fourier transformation is applied to the mechanical excitation signals f (t) and to the mechanical response signals x (t),
the transfer function T (w) is calculated by dividing the Fourier transform of the mechanical response signal by the Fourier transform of the mechanical excitation signal,
said transfer function (20) having peaks corresponding respectively to the resonant frequency of the block (4) at the heaving and to the resonant frequency of the post (1) in the axial vibration mode,
we seek the theoretical curve (21) closest to the transfer function (20) calculated and which materializes the transfer function of a system (6) with two degrees of freedom, respectively modeling the mass of mass M and the post of mass m,
we identify the constants (residue r1, resonance w1 and w2 and damping) of this theoretical curve (21),
the mass m of the foundation mass (4) is determined using the approximate formula: $$\text{M = 1 / r1 - (1 - (w1 / w2) ²) ⁻²m}$$

and we determine the stiffness K of the soil / solid connection K using the exact formula:

formula which can advantageously be substituted, in the usual cases, the approximate formula: $$\text{K = m w1².}$$

Method according to claim 1, characterized in that the vertical shock is applied to the upper face (12) of the foundation block (4) near the base of the post (1). A method according to claim 2 characterized in that said vertical shock is applied using an impactor (hammer or falling mass) (14) instrumented by a force sensor. Method according to either of Claims 2 and 3, characterized in that the mechanical response signals of the block (4) are measured by measuring the speed or the vertical acceleration of the block (4) at several points close to the base of the post. (1) and by averaging the measured speeds or accelerations. Method according to Claim 4, characterized in that the speed or vertical acceleration of the massif (4) is measured using a motion sensor (17) (geophone or accelerometer). Method according to any one of Claims 2 to 5, characterized in that the Fourier transforms of the mechanical excitation and speed (or acceleration) signals measured during several successive shocks are averaged before calculating the transfer function. Method according to any one of Claims 1 to 7, characterized in that the values of the measurements of mechanical excitation and mechanical response signals are stored on a magnetic medium, while the values stored by a computer are processed ( 16) and in that the closest theoretical curve (21) is sought using software known as "modal analysis or parametric identification". Device for implementing the method according to any one of the preceding claims, characterized in that it comprises:
an impactor (hammer or falling mass) (14) intended to be used to give vertical shocks to the foundation mass (4) and instrumented by a force sensor measuring the force of the impact,
at least one motion sensor (geophone or accelerometer) (17) intended to measure the speed or the acceleration of vertical movement of the foundation mass (4) under the action of the impactor impact (14),
a microcomputer connected to the impactor force sensor and to the motion sensor via interfaces, digitizing the signals received from them corresponding to the impact force of the impactor and to the speed or acceleration displacement of the block (4) as a function of time, and capable of calculating the mass M of the foundation block (4) and the stiffness of the soil / block connection K using appropriate programs.

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